NEET Chemistry Structure Of Atom Resoulution Of Vectors MCQs

A particle is projected with velocity $\vec{v} = (6\hat{i} + 8\hat{j})$ m/s. If $g = 10 m/s^2$, the radius of curvature of its trajectory at the highest point is:

Two vectors $\vec{A}$ and $\vec{B}$ have magnitudes A and B respectively. If the magnitude of their resultant is $\sqrt{A^2 + B^2 + \sqrt{3}AB}$, the angle between the vectors is:

A force $\vec{F} = (3\hat{i} + 4\hat{j} - 5\hat{k})$ N acts on a particle causing a displacement $\vec{s} = (2\hat{i} - \hat{j} + 3\hat{k})$ m. The work done by the force is:

A river flows due east with a speed of 3 m/s. A man can swim in still water at a speed of 5 m/s. If he wants to cross the river in the shortest possible time, the angle at which he should swim with respect to the north is:

Three forces $\vec{F_1} = 2\hat{i} - 3\hat{j}$, $\vec{F_2} = -5\hat{i} + \hat{j}$, and $\vec{F_3} = a\hat{i} + b\hat{j}$ act on a particle. If the particle is in equilibrium, the values of a and b are:

A projectile is launched with an initial velocity $v_0$ at an angle $heta$ with the horizontal. At the highest point of its trajectory, the ratio of its potential energy to its kinetic energy is:

A vector has a magnitude of 5 units and is directed along the positive x-axis. What are its components?

A vector $\mathbf{A}$ has components (3, 4). What is its magnitude?

A force of 10 N acts at an angle of 30° with the horizontal. What is the horizontal component of the force?

Which of the following represents the vertical component of a vector $\mathbf{V}$ with magnitude $V$ and angle $heta$ with the horizontal?